Quartic Polynomial
A quartic polynomial is a polynomial of degree 4, which means the highest power of the variable in the polynomial is 4. The general form of a quartic polynomial is:
f(x) = ax4 + bx3 + cx2 + dx + e
Where a, b, c, d, and e are constants, and x is the variable. The coefficient 'a' must not be equal to 0, otherwise, it would not be a quartic polynomial.
Key Concepts:
- Degree: The degree of a quartic polynomial is 4, which is the highest power of the variable.
- Leading Coefficient: The coefficient 'a' in the term ax4 is called the leading coefficient.
- Roots: A quartic polynomial equation may have up to 4 roots or solutions.
- Graph: The graph of a quartic polynomial is a curve with up to 3 turning points.
Examples:
Example of a quartic polynomial: f(x) = 2x4 - 3x3 + 5x2 + 2x - 7
Another example: f(x) = x4 - 4x3 + 6x2 - 4x + 1
Study Guide:
When studying quartic polynomials, it's important to understand the following:
- How to identify the degree of a polynomial and determine whether it's a quartic polynomial.
- Finding the leading coefficient of a quartic polynomial.
- Identifying the roots or solutions of a quartic polynomial equation.
- Graphing a quartic polynomial and understanding its characteristics such as turning points.
Understanding these concepts and practicing solving problems related to quartic polynomials will help you master this topic.
Good luck with your studies!
.◂Math Worksheets and Study Guides Fifth Grade. Order of Operations
Study Guide
Order of Operations 
Activity Lesson
Decoding Equations Worksheet/Answer key
Order of Operations Worksheet/Answer key
Order of Operations Worksheet/Answer key
Order of Operations Worksheet/Answer key
Order Of Operations
Activity LessonWorksheet/Answer keyWorksheet/Answer keyWorksheet/Answer keyWorksheet/Answer keyThe resources above cover the following skills:
Algebra (NCTM)
Use mathematical models to represent and understand quantitative relationships.
Model problem situations with objects and use representations such as graphs, tables, and equations to draw conclusions.
Connections to the Grade 5 Focal Points (NCTM)
Algebra: Students use patterns, models, and relationships as contexts for writing and solving simple equations and inequalities. They create graphs of simple equations. They explore prime and composite numbers and discover concepts related to the addition and subtraction of fractions as they use factors and multiples, including applications of common factors and common multiples. They develop an understanding of the order of operations and use it for all operations.